priorly: https://no-outlet.com/@ivlia/116336755502734396
Proposition 1: If there were one altitude of two rectilinear superficies of equidistant sides or of triangles, then either of them will be so much to the other as its base is to the base of the other.
Proposition 25: If there were [four] proportional quantities, and the first of them were the greatest and the last were the least, the first and last accepted together are necessarily understood to be greater than the other two.
nb: book v ends at prop 25 but if you can believe it (& I certainly can!) Campanus addends his interpretation of the material with 9 propositions of his own, which hereafter will be tagged as "Campanean" (as opposed to "Euclidean") geometry.
Proposition 24: If the proportion of the first to second were as third to fourth, and the proportion of the fifth to second were as sixth to fourth, then the proportion of the first and fifth accepted together to the second will be as the sixth and third accepted together to the fourth.
Proposition 23: If there were however many quantities to some others according to their number, of which any two were indirectly proportioned according to the proportion of two from the prior, the proportions will be in equal proportionality.
Proposition 22: If there were however many quantities to some others according to their number, of which any two were in equal proportionality according to the proportion of two from the first, they will be proportional.
Proposition 21: If there were however many quantities to any others according to their number, of which any two from the prior and any two from the posterior were each compared perversely according to their proportion, it is likewise necessary in a proportionality of equality that if the first of the prior be greater than the last, then the first of the posterior shall be greater than the last. And if less, then less. And if equal, then equal.
Proposition 20: If there were however many quantities to any others according to their number, of which each of the two prior are according to the proportion of the two posterior, it is necessary there be a certain equality in proportionality, so if the first of the prior were greater than the last, the first of the posterior shall be greater than the last. And lesser if lesser, and equal if equal.
Proposition 19: If two portions are abscinded from two totals, and the total to total were as the abscinded is to abscinded, then the remainder to remainder will be as the total is to total.
Proposition 18: If quantities were disjointedly proportional, they will also be conjoinedly proportional.
Proposition 17: If quantities shall be conjointly proportional, the same are likewise disjointedly proportional.
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